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Gear rack problem

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The gear rack has a mass of 6 kg, and the gears each have a mass of 4 kg and a radius of gyration k = 30 mm at their centers. If the rack is originally moving downward at 2 m/s, when s = 0, determine the speed of the rack when s = 600 mm. The gears are free to turn about their centers, A and B.

(See attached file for fig. and full problem description).

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The solution provides a step-by-step explanation that determines the speed of the rack that is originally moving downward.

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